Yet, for all intents and purposes, I think that most people would still consider
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a dead body re-animated by an evil spirit to be, essentially, a zombie, unless the spirit started doing things well beyond normal zombie behaviour. . . then it might be deemed a lich, a ghoul, a vampire, a haint etc. etc., but, in any event, undead and or living dead still seems to apply well enough, though I am not particularly keen on the idea of an undead Azog running around.

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We have unsubstantial ghosts, living beings that have faded, and possibly evils spirits using corpses as puppets.

We don't see the D&D idea of flesh-robots: animated corpses with no mind or spirit at all. Nor do we see a specific spirit of a dead being reanimating it's own corpse, as appears to be the case with Azog.

"Hear me, hounds of Sauron, Gandalf is here! Fly if you value your foul skins, I will shrivel you from tail to snout if you step within this circle!"

"Do not be to eager to deal out death in judgement. Even the very wise cannot see all ends."